2011-04-15T00:00:30 sometimes i think it's nice to have like reset() and reset(value) 2011-04-15T00:00:49 i don't miss things like that 2011-04-15T00:00:59 it's a bother to remember lots of function names to do almost the same thing 2011-04-15T00:01:04 nah 2011-04-15T00:01:36 in haskell, functions are small anyway. the very idea of reset() is that it's probably just reset(value) with a default value 2011-04-15T00:01:59 so instead of having multiple versions of reset, you could generalize over values that have default values 2011-04-15T00:02:05 *types that have default values 2011-04-15T00:02:28 and then have a very generic reset function 2011-04-15T00:02:47 i made some assumptions about the intent there, i guess 2011-04-15T00:03:21 yeah okay 2011-04-15T00:04:52 i guess the point i'm trying to make is that in haskell your goal is to write small, composable functions. functions that are nothing more than other functions with default arguments might be a warning sign a lot of the time 2011-04-15T00:06:14 a warning that its interface is too complicated and that some of the arguments could be inferred by type, perhaps 2011-04-15T00:26:29 *** McLeopold has quit IRC (Quit: Leaving.) 2011-04-15T01:11:05 wow, gedit is a pretty good latex editor anyway 2011-04-15T01:14:56 nevermind 2011-04-15T01:15:04 it was opening them in LaTeXilla :P 2011-04-15T01:21:44 *** antimatroid has quit IRC (Read error: Connection reset by peer) 2011-04-15T01:22:00 *** antimatroid has joined #aichallenge 2011-04-15T01:32:52 lol 2011-04-15T01:55:24 *** Stocha has joined #aichallenge 2011-04-15T02:00:10 *** delt0r_ has joined #aichallenge 2011-04-15T02:00:38 *** jaycobcoleman has joined #aichallenge 2011-04-15T02:00:43 *** ahmedhelal has quit IRC (Read error: No route to host) 2011-04-15T02:01:08 *** ahmedhelal has joined #aichallenge 2011-04-15T02:01:19 *** delt0r___ has quit IRC (Ping timeout: 246 seconds) 2011-04-15T02:20:08 *** ltriant has quit IRC (Ping timeout: 250 seconds) 2011-04-15T02:22:01 *** ltriant has joined #aichallenge 2011-04-15T02:23:15 *** chris__0076 has joined #aichallenge 2011-04-15T02:26:18 *** Chris_0076 has quit IRC (Ping timeout: 276 seconds) 2011-04-15T02:43:42 *** Stocha has quit IRC (Ping timeout: 252 seconds) 2011-04-15T02:49:26 *** Ttech has quit IRC (Read error: Operation timed out) 2011-04-15T02:53:46 I have a question about the damage battle option for anyone who can answer it 2011-04-15T02:54:30 Will the damage of each ant be reset after the battle is resolved or is it permanent? 2011-04-15T02:55:46 reset 2011-04-15T02:55:56 *** dr- is now known as lotus 2011-04-15T02:55:57 lovely, thank you 2011-04-15T02:56:03 we don't want to complicate it like that 2011-04-15T02:56:03 *** lotus is now known as dr- 2011-04-15T02:56:25 good, that would be quite a pain. Much more strategy involved this way 2011-04-15T02:56:40 yep, the rule has been chosen to be interesting strategy wise 2011-04-15T02:56:58 the power method was perhaps more interesting imo, but people didn't understand it easily enough, so this was a great compromise 2011-04-15T02:57:16 I was rooting for either this or power. Really anything but itterative. 2011-04-15T02:57:23 I really liked power 2011-04-15T02:57:24 yep :P 2011-04-15T02:57:39 power was my favourite, up until damage i was fighting fiercely for power 2011-04-15T02:57:48 i also fought fiercely to get row,col indexing 2011-04-15T02:58:00 i simply can't understand why anyone would do x,y indexing, it's inferior 2011-04-15T02:58:28 why so inferior? 2011-04-15T02:58:47 because if you read a char map from file, or output it, you need to transpose the map 2011-04-15T02:58:54 with row,col indexing it's always the same 2011-04-15T02:59:06 not if you turn the monitor sideways 2011-04-15T02:59:12 :P 2011-04-15T02:59:15 haha good point 2011-04-15T02:59:17 it makes life more confusing imo 2011-04-15T02:59:54 You make a compelling argument 2011-04-15T03:00:19 that's one of my more solid arguments over something pedantic :P 2011-04-15T03:00:57 You can be as pedantic as you'd like as long as you can back it up 2011-04-15T03:01:30 i'm often clutching at straws i think :P 2011-04-15T03:02:42 I think it's a tendency of sciency people to become overly-opinionated on every issue 2011-04-15T03:03:51 *** Ttech has joined #aichallenge 2011-04-15T03:04:11 yep, i always say it comes from my lecturers tearing me to pieces with assignment flaws 2011-04-15T03:04:32 and i love every minute of it :) 2011-04-15T03:05:03 i lost marks in second year algebra for my grammar not being right 2011-04-15T03:05:08 what is your role in the aichallenge? You seem to be fairly active. 2011-04-15T03:05:21 participant that helps out a bit 2011-04-15T03:05:54 Didn't you write one of the starters? 2011-04-15T03:06:00 i wrote the c++ starter 2011-04-15T03:06:07 i also did the random walk symmetric maps 2011-04-15T03:06:12 and helped work out a lot of the rules 2011-04-15T03:06:33 There we go, I've looked through the C++ starter quite thouroughly 2011-04-15T03:06:43 anything you hate? 2011-04-15T03:06:50 i use the communist approach to programming 2011-04-15T03:06:53 everything is public 2011-04-15T03:07:15 Nope, everything looks pretty good to me 2011-04-15T03:07:35 But honestly I'm not a beacon of experience 2011-04-15T03:07:46 i'm not a very experienced programmer 2011-04-15T03:08:20 depending on what one considers as experienced, i wouldn't consider myself experienced anyway 2011-04-15T03:08:51 I find my efforts to learn programming constantly being thwarted by school 2011-04-15T03:09:08 and sleeping 2011-04-15T03:11:07 i've learnt c++ mostly from these contests and writing my own game theory library 2011-04-15T03:11:34 i don't know anything else well, i can hack stuff together in python now 2011-04-15T03:11:46 (very) slowly trying to grasp haskell 2011-04-15T03:12:51 yeah my knowledge base is mostly split between c++ and python 2011-04-15T03:13:00 and bash 2011-04-15T03:15:43 you're still allowed to compete, right? 2011-04-15T03:17:47 yep 2011-04-15T03:17:56 anyone that doesn't have access to the severs can compete 2011-04-15T03:18:05 it was pretty much allow that or have no one to work on the game 2011-04-15T03:18:27 everything we know/can access is public information/open source 2011-04-15T03:19:21 I would imagine writing a game theory library would be pretty useful experience. Have you done much work on your own bot? 2011-04-15T03:20:43 *** ltriant has quit IRC (Quit: Computer has gone to sleep) 2011-04-15T03:23:59 it's not that relevant to these contests, i have played around a bit with food collection but not heaps 2011-04-15T03:24:18 i have been pretty busy at uni lately, and i may be doing gsoc which will render me quite busy 2011-04-15T03:24:53 *** needsch has joined #aichallenge 2011-04-15T03:25:49 Oh man, I would love to do gsoc, but I don't think it's open to high school students 2011-04-15T03:26:09 how far off uni are you? 2011-04-15T03:26:26 where do you live? 2011-04-15T03:26:56 Alaska 2011-04-15T03:27:05 I'm a senior in high school 2011-04-15T03:27:14 what year is that? 2011-04-15T03:27:25 high school is years 7-10 where i live :P 2011-04-15T03:27:27 4th and final 2011-04-15T03:27:45 then college is year 11 and 12 (not uni), then uni 2011-04-15T03:28:14 hmm. We've got middle school for 7 and 8, the 9-12 is high school 2011-04-15T03:29:27 we have elementary = {kinder, prep, 1, 2}, primary = elementary or {3,...,6}, high = {7,..,10} and college = {11,12} 2011-04-15T03:29:49 tasmania <3 2011-04-15T03:30:02 Ah, I was about to ask 2011-04-15T03:30:53 That's very cool. I had no idea that's how school was down there 2011-04-15T03:31:15 it took me a while to work out college = uni in the us when i was younger 2011-04-15T03:31:45 What are you doing for gsoc? 2011-04-15T03:32:17 if i get it, enumerating nash equilibria for 2 player extensive form games with imperfect information using the sequence form of the game with gambit 2011-04-15T03:32:23 antimatroid: you don't call 11-12 high school? 2011-04-15T03:32:31 sigh: no 2011-04-15T03:32:38 how odd 2011-04-15T03:32:47 it's nice not having the younger people around the 11-12 campus 2011-04-15T03:32:52 they can be more chilled with you 2011-04-15T03:33:00 where are you from sigh? 2011-04-15T03:33:04 melbourne 2011-04-15T03:33:10 for a couple of days anyway :P 2011-04-15T03:33:18 a day* 2011-04-15T03:33:20 :) 2011-04-15T03:33:41 why's this? 2011-04-15T03:33:52 why is what? 2011-04-15T03:34:05 he is moving to sydney 2011-04-15T03:34:15 oh, that, yes 2011-04-15T03:34:43 anyway, college doesn't have a specific meaning here... some high schools are called colleges and the dorms that uni students stay in are called colleges 2011-04-15T03:34:57 yeah 2011-04-15T03:35:14 *** needsch has quit IRC (Quit: Leaving.) 2011-04-15T03:35:20 jaycobcoleman: what are you planning to do at uni? 2011-04-15T03:35:30 *** aerique has joined #aichallenge 2011-04-15T03:35:59 well there was the consideration of something relating to engineering, but now I'm starting to lean more toward something involving programminf 2011-04-15T03:36:42 doesn't have to be either/or there 2011-04-15T03:36:52 indeed it doesn't 2011-04-15T03:38:26 animatroid: To be entirely honest, I have no idea what your gsoc plan entails 2011-04-15T03:40:27 *** antimatroid1 has joined #aichallenge 2011-04-15T03:40:35 *** antimatroid has quit IRC (Read error: Connection reset by peer) 2011-04-15T03:41:17 reincarnated? 2011-04-15T03:41:19 an extensive form game is a tree representation of a game 2011-04-15T03:41:58 then nash equilibria are strategies where no player can alter their strategy to increase their payoff, given what the other players are doing 2011-04-15T03:42:03 do maths at uni :P 2011-04-15T03:42:07 maths is awesome 2011-04-15T03:43:07 agreed. I'm in my second year of calculus at the moment 2011-04-15T03:43:32 it gets a lot more fun once you get to algebra and analysis ;) 2011-04-15T03:44:17 although don't do just maths, do maths and (engineering/cs/physics/something) 2011-04-15T03:45:35 I'm starting to put some heavy consideration on math + cs 2011-04-15T03:46:02 it's a strong combination 2011-04-15T03:46:19 i'm heavily biased though :P 2011-04-15T03:46:54 yup, cs in particular is a strong combination with anything, because now everything involves a lot of computation 2011-04-15T03:47:32 Not sure wether I want to go micro or macro when it comes to computers and programming though 2011-04-15T03:47:46 what do you mean? 2011-04-15T03:47:46 micro or macro? 2011-04-15T03:48:02 algorithms! 2011-04-15T03:48:12 learn your algorithms well 2011-04-15T03:48:25 well, algorithms are the basis for any cs course 2011-04-15T03:49:52 and algorithms is usually the first "real" cs subject that students will encounter 2011-04-15T03:50:23 I don't suppose any thought at all has gone into the next ai challenge, has it? 2011-04-15T03:53:38 what do you mean? 2011-04-15T03:53:46 i think we have a game for the following contest 2011-04-15T03:54:01 specifically warlight 2011-04-15T03:54:23 *** smellyhippy has quit IRC (Ping timeout: 240 seconds) 2011-04-15T03:54:52 that answers my question beautifully 2011-04-15T03:56:08 *** amstan has quit IRC (Ping timeout: 260 seconds) 2011-04-15T03:56:09 I ask because if I stay as interested in learning about programming in the future as I am now I think I'll want to and be very much able to help out with various aspects of the competition 2011-04-15T03:59:42 feel free to play around with making maps for ants 2011-04-15T03:59:51 we want as many types of maps as possible 2011-04-15T04:00:15 if you want to do symmetric maps, take a look at how my symmetric map gen picks out the dimensions and tiles the maps 2011-04-15T04:01:27 sigh: http://www.overclockers.com.au/pic.php?pic=images/newspics/15apr11/22.jpg :) 2011-04-15T04:05:06 antimatroid1: there is nothing logically impossible about the first two :P 2011-04-15T04:05:07 *** jaycobcoleman has quit IRC (Ping timeout: 252 seconds) 2011-04-15T04:05:52 you say that like i understood any but the last :P 2011-04-15T04:06:01 you can have a more machine more powerful than a Turing machine that it can solve the halting problem for turing machines 2011-04-15T04:06:40 and qm is a scientific theory, which though very very well tested and verified, is not logically proven 2011-04-15T04:08:19 lol "Were you in Australia on 30 April 2011?" 2011-04-15T04:08:20 antimatroid1: you should at least know the first one :P 2011-04-15T04:08:27 o_O 2011-04-15T04:08:34 well, were you? 2011-04-15T04:08:50 i've never done any of that stuff, i have a few gaping holes that need to be filled 2011-04-15T04:08:59 i'm going to do theory of computation at anu next year hopefully 2011-04-15T04:09:09 it's on the graduate survey 2011-04-15T04:09:29 ah yeah, theory of computation is fun 2011-04-15T04:09:45 2: Would you describe yourself as having a disability? 2011-04-15T04:09:46 ahaha 2011-04-15T04:09:54 they chose some strange wording of things 2011-04-15T04:10:00 yeah... 2011-04-15T04:10:19 trying not to offend anyone? 2011-04-15T04:12:01 yeah 2011-04-15T04:14:05 *** Stocha has joined #aichallenge 2011-04-15T04:14:33 sigh: what do you mean more powerfull than turing machine than can solve halting for turning machines ? 2011-04-15T04:15:49 there is nothing impossible about being able to solve the halting problem for Turing machines, it is impossible to solve the halting problem for turing machines *on a turing machine itself* 2011-04-15T04:16:27 does it exists a machine that a machine turing can not emulate ? 2011-04-15T04:16:55 Or any solver of halting system that a machine turing can not emulate. 2011-04-15T04:16:57 mathematically, of course... you can define such a machine into existance 2011-04-15T04:17:11 physically, dunno... maybe, maybe not 2011-04-15T04:17:11 turing machin is pretty strong stuff already. With unlimited time and space. 2011-04-15T04:17:23 how do you define it mathematically ? 2011-04-15T04:18:41 I define a an oracle X which takes as an input a turing machine program, and outputs 1 if it halts, and 0 if it doesn't 2011-04-15T04:19:20 so X is function 2011-04-15T04:19:27 then if I combine that with a normal turing machine, I have a machine that is more powerful than a turing machine 2011-04-15T04:19:47 sure, only catch is that X cannot be computed on a turing machine 2011-04-15T04:20:08 but there's nothing stopping me from assuming one exists 2011-04-15T04:20:15 is there not ? 2011-04-15T04:20:34 there is nothing for stopping me assuming a set of all ordinal number exists. 2011-04-15T04:20:45 except mathematicians i suppose :p 2011-04-15T04:21:44 I am not familiar with that, but as long as it is not logically inconsistent, then fine 2011-04-15T04:22:00 it is said to be logically inconsistent :p 2011-04-15T04:22:09 ok, in which case then you can't 2011-04-15T04:22:20 So the question is, how do we now that supposing X exists is not logically inconsistent 2011-04-15T04:22:34 there is nothing inconsistent about my oracle X, although the halting problem proves that it can't be implemented on a turing machine 2011-04-15T04:22:53 nothing inconsistent, it has a well-defined input and output 2011-04-15T04:23:09 yeah so does the X function on a turing machine 2011-04-15T04:23:19 yet mathematicians say it is inconsistent there 2011-04-15T04:23:36 so having input and output is not enough to make it true. 2011-04-15T04:23:53 but I am not saying that X has to run on a turing machine 2011-04-15T04:24:06 yeah 2011-04-15T04:24:16 I am saying that it exists, that's all... if I assume that it exists than I have created a more powerful machine 2011-04-15T04:24:20 Stocha: its a well known fact that oracles are not subject to turing machine limitations 2011-04-15T04:24:22 but when you add that, you do not have immediatly the fact it is not possible 2011-04-15T04:24:44 which has it's own halting problem, but it's powerful enough to solve the problem for turing machines 2011-04-15T04:25:11 what does halting problem mean with an oracle ? 2011-04-15T04:25:20 it means it won't output anything ? 2011-04-15T04:25:28 but you said it will output either 1 or 0 2011-04-15T04:26:18 delt0r_: oracle are not well known to me yet. 2011-04-15T04:26:53 yes it will output 1 or 0 because it is a more powerful machine than a Turing machine 2011-04-15T04:29:06 the catch is that you can't feed oracle X a program which uses the oracle X as part of its program 2011-04-15T04:29:47 which is why the normal proof of the halting problem doesn't work for oracle X 2011-04-15T04:31:11 *** Naktibalda has joined #aichallenge 2011-04-15T04:33:43 is the oracle a turing machine ? :p 2011-04-15T04:33:49 i didn't get that part in wikipedia 2011-04-15T04:34:16 what does "finitely many" means ? 2011-04-15T04:34:19 Stocha: it cannot be implemented on a turing machine, the halting problem is proof of that 2011-04-15T04:34:24 is that finite or infinite ? 2011-04-15T04:35:01 Yeah, but i suddenly wonder about a turing machine using another one as an oracle. 2011-04-15T04:35:07 what context is "finitely many" is used in? 2011-04-15T04:35:36 if you combine a turing machine with such an oracle then you create a more powerful machine 2011-04-15T04:35:50 e oracle machine is initialized with the work tape containing some input with finitely many 1's and the rest of the tape blank, 2011-04-15T04:36:23 yeah, the tape has a finite number of 1s 2011-04-15T04:37:05 but they can be anywhere ? 2011-04-15T04:37:16 i mean there is no bound to how deep they can be ? 2011-04-15T04:37:36 so you can search forever the tape, and have no guartees that you found all ? 2011-04-15T04:37:52 wich means you can't count them 2011-04-15T04:38:22 I'm not sure of the significance of that statement, so I can't really answer you 2011-04-15T04:38:32 okay fair enough :) 2011-04-15T04:38:47 the subject is time consuming though. and not very promising i suppose. 2011-04-15T04:39:24 I was wondering about what a tape with a finite number of 1 looked like. 2011-04-15T04:39:29 what's an oracle? 2011-04-15T04:39:32 infinite tape. 2011-04-15T04:40:11 then because i now there exists N that bound the number of 1 on the infinite tape, i wanted to find N. 2011-04-15T04:40:25 so i went like : let's run along the tape and find what N is. 2011-04-15T04:40:28 but i never found it :p 2011-04-15T04:41:01 i did :p 2011-04-15T04:41:20 how did you ? 2011-04-15T04:41:25 antimatroid1: an oracle is a black-box which computes a well-defined function 2011-04-15T04:41:35 so it's a function? 2011-04-15T04:42:00 oracle:dataSet->answerSet? 2011-04-15T04:42:05 bloody smileys 2011-04-15T04:42:19 in some contexts it is the function, in other contexts it is a turing machine combined with the function 2011-04-15T04:43:01 *** Eruonen has joined #aichallenge 2011-04-15T04:44:16 Stocha: don't read so much into it... all it is saying that the the initial state can't have an infinite number of 1s 2011-04-15T04:44:28 *** needsch has joined #aichallenge 2011-04-15T04:45:36 what's the difference between a tape than can have an infinite number of one, and one that can't have but still can have some 1 2011-04-15T04:46:04 well i guess it is, if you run indefinetly you'll always find some 0 in a finite number of step 2011-04-15T04:46:38 if the tape is initialised with a finite number of 1s, then you can define it in a finite amount of space, for example 2011-04-15T04:46:54 the program obviously knows how many 1s there are 2011-04-15T04:46:56 why ? 2011-04-15T04:47:02 ah 2011-04-15T04:47:04 why what? 2011-04-15T04:47:17 nothing :p 2011-04-15T04:47:48 hum something puzle me there. 2011-04-15T04:47:52 hmm... actually 2011-04-15T04:48:08 Stocha: I was wrong 2011-04-15T04:48:34 how do you proove yourself wrong on this one ? 2011-04-15T04:48:38 the program doesn't know... the finite number of 1s just guarantees that the thing halts :P 2011-04-15T04:48:57 I think... hmmm 2011-04-15T04:49:19 let me look at it more 2011-04-15T04:50:08 That all tapes with a finite number of 1 can be defined in a finite amount of space. 2011-04-15T04:50:17 that's the question right ? 2011-04-15T04:50:19 oh, that is true 2011-04-15T04:50:54 I'm just trying about what the program knows about the initial state... and what it does 2011-04-15T04:50:57 Are those tapes even countables ? 2011-04-15T04:51:38 what tapes? 2011-04-15T04:51:50 infinite tapes with finetly mana 1 2011-04-15T04:53:39 well, if you don't know how many 1s there are beforehand you can't count them... but I don't see why that is a problem 2011-04-15T04:54:51 if there the set of infinite tapes with finetely many 1 as a cardinality > N, i doubt you will be able to show each tape can be defined in a finite amount of space :p 2011-04-15T04:55:14 *** needsch has quit IRC (Quit: Leaving.) 2011-04-15T04:55:19 > card (Set of all integer) 2011-04-15T04:56:25 i think there exists a bijection between the set of "infinite tapes with finetly many 1" and R the set of all real number. 2011-04-15T04:56:54 in wich case i don't think you'll be able to define each tape in a finite amount of information. 2011-04-15T04:56:58 no, the bijection exists between them and the integerss 2011-04-15T04:57:10 ? 2011-04-15T04:57:25 why isn't it obvious to me then :'( 2011-04-15T04:58:09 every tape with a finite number of ones encodes an integer (in binary), and an integer can be encoded on a tape with a finite number of ones. 2011-04-15T04:58:54 yeah but i'm not sure i encodes an integer :p 2011-04-15T04:58:58 it 2011-04-15T04:59:23 why aren't you sure? 2011-04-15T04:59:25 the set of all binary integer. 2011-04-15T04:59:40 well because. well. 2011-04-15T04:59:45 mm gnn 2011-04-15T05:00:09 each tape has P (the number of 1) as characteristic 2011-04-15T05:00:25 ok... 2011-04-15T05:01:07 but the tape is infinite 2011-04-15T05:01:23 ok... 2011-04-15T05:01:27 you have no garantee to go from first 1 to second one in a finite number of step do you ? 2011-04-15T05:01:40 never was that stated at least. 2011-04-15T05:01:56 that's why you can't count the number of 1. 2011-04-15T05:02:04 i think. 2011-04-15T05:02:16 if the is a second 1, then you will reach it in a finite number of steps 2011-04-15T05:02:46 *if there is a second 1 2011-04-15T05:02:48 but you can't decide if there is in a finite number of steps 2011-04-15T05:03:04 if you don't know the number of 1s beforehand, sure 2011-04-15T05:03:32 but you have the same problem with integers... if you encode an integer on a tape, you never know if it is finished 2011-04-15T05:03:37 it's like let's say it's an integer (binary) with only 0 or 1 One 2011-04-15T05:03:39 *** chris___0076 has joined #aichallenge 2011-04-15T05:03:58 yeah but that's not an integer. 2011-04-15T05:04:03 that's something else. 2011-04-15T05:04:39 why isn't it an integer? 2011-04-15T05:05:03 let's say an integer is 1 or 0 for a finite number of step. 2011-04-15T05:05:21 then tapes with 1 or 0 in every step do not define integers. 2011-04-15T05:05:49 *** chris__0076 has quit IRC (Ping timeout: 246 seconds) 2011-04-15T05:05:54 they do if you constrain the number of 1s to be finite :) 2011-04-15T05:06:23 i don't see why there can't be an infinite number of 0 then. 2011-04-15T05:07:00 imagine the integer written backwards 2011-04-15T05:07:07 yeah. 2011-04-15T05:07:16 ...005 = 5 2011-04-15T05:07:23 for low meaning to high meaning yes. 2011-04-15T05:07:27 from 2011-04-15T05:08:19 having 0s (even an infinite number of 0s) in front of an integer does not change the value :P 2011-04-15T05:08:20 integer have a finite number of characters to write them 2011-04-15T05:08:40 depends on your representation 2011-04-15T05:09:00 you can't represent integers in a finite number of characters in base pi, for example :P 2011-04-15T05:09:23 integer are such that after a finite number of step, it is always the same caracter :p 2011-04-15T05:09:46 ah you can't do that ? 2011-04-15T05:09:54 can't do what? 2011-04-15T05:10:33 integer in base pi are not integers :p 2011-04-15T05:10:41 why not? 2011-04-15T05:10:42 they are reals numbers :p 2011-04-15T05:11:10 because they have infinite numbers of characters without them being all 1 or 0 after a finite number of step. 2011-04-15T05:11:22 you are confusing the objects with the representation 2011-04-15T05:11:31 am i. 2011-04-15T05:11:45 yes 2011-04-15T05:11:51 i have always used this system :p 2011-04-15T05:12:06 How do you write 2 in base pi ? 2011-04-15T05:12:37 i'm not familiar with those bases. 2011-04-15T05:12:46 never encountered them yet. 2011-04-15T05:12:52 ok, 2 in base pi is just 2... 2011-04-15T05:13:09 ? 2011-04-15T05:13:14 this is my favorite irrational base: http://en.wikipedia.org/wiki/Golden_ratio_base 2011-04-15T05:13:27 but integers have finite representation there :) 2011-04-15T05:15:16 all non-negative integers have a unique representation as a terminating (finite) base-φ expansion 2011-04-15T05:15:27 what does that phrase means ? 2011-04-15T05:15:58 what part don't you understand? 2011-04-15T05:16:08 what's finite in there ? 2011-04-15T05:16:23 the length of the sting representing the number 2011-04-15T05:16:27 what's a base phi expansion ? 2011-04-15T05:16:41 so you are saying there a finite number of characters for representing integers ? 2011-04-15T05:17:15 so my system hold to that base :p 2011-04-15T05:17:16 9 in base phi is "10010.0101" which is 10 characters long which is finite 2011-04-15T05:17:22 sure 2011-04-15T05:17:45 but that's just a nice property of base phi 2011-04-15T05:17:57 you wanted to show me there exists bases where integers cannot be represented with finite amount fo characters 2011-04-15T05:18:57 base pi is an example if your numbers are greater than 3 2011-04-15T05:19:13 ah okay 2 was special case then :p 2011-04-15T05:22:04 4 in base pi is approximately 10.2201... 2011-04-15T05:22:11 http://www.dwheeler.com/essays/bases.html 2011-04-15T05:22:22 i don't really get what irrationnal bases are yet :p 2011-04-15T05:23:21 4 = 1*pi + 0*pi^0 + 2*pi^-1 + 2*pi^-2 + 0*pi^-3 + 1*pi^-4 + .... 2011-04-15T05:23:57 what about 3 then ? 2011-04-15T05:24:36 i saw a compelling argument the other day for defining tau = 2pi 2011-04-15T05:25:16 Stocha: I am implicitly saying that the symbols we are using are 0,1,2,3 so 3 just equals 3 :) 2011-04-15T05:25:26 antimatroid1: sure let's re-write all the textbooks :P 2011-04-15T05:25:36 sigh: don't need to 2011-04-15T05:25:43 just start writing new ones using tau 2011-04-15T05:26:38 physicist wont be happy, they already use tau for a bunch of other stuff :P 2011-04-15T05:27:06 i don't care for physicists :P 2011-04-15T05:27:21 how many symbols are we using sigh ? 2011-04-15T05:27:29 what i find annoying is some game theory texts using Sigma for the set of mixed strategies 2011-04-15T05:27:56 imo Sigma should be reserved for summations 2011-04-15T05:28:17 for base pi? just 0,1,2,3 and the decimal point, so 5 I suppose 2011-04-15T05:28:42 antimatroid1: oh, you aren't going to like the definition of turing machines then :P 2011-04-15T05:29:26 those muggles 2011-04-15T05:29:45 Sigma is used for the input alphabet of the tape 2011-04-15T05:30:08 yeah i just checked the wiki page 2011-04-15T05:30:14 well, in theory of computation in general 2011-04-15T05:30:30 not just turing machines 2011-04-15T05:30:44 yeah, i can live with it, but i wouldn't have personally made that choice 2011-04-15T05:30:55 :P 2011-04-15T05:31:16 i would go so far as to say i would slap the person who did if given the change :P 2011-04-15T05:31:23 chance** 2011-04-15T05:31:30 in base Pi you should have Pi symbols don't you ? 2011-04-15T05:31:49 or we go for two symbols. 2011-04-15T05:31:51 why 5 ? 2011-04-15T05:32:31 well, 4 really... 5th was just decimal point for completeness :P 2011-04-15T05:33:37 Stocha: just by convention, we extend the concept of a positional number system by changing the base, but keeping the symbols as integers 2011-04-15T05:34:10 *non-negative integers 2011-04-15T05:34:32 of course, you can relax that constraint such as in systems like balanced ternary: http://en.wikipedia.org/wiki/Balanced_ternary 2011-04-15T05:35:56 if you like, I can specify that I was talking about base pi, using the digits {0,1,2,3} 2011-04-15T05:39:50 okay 2011-04-15T05:40:04 in general, a positional number system has a set of digits S and a base B, any a number is represented as a string with a finite number of digits before the decimal point and a possibly infinite number after: eg "abc.def..." is equal to a*B^2+b*B^1+C*B^0+D*B^-1+E*B^-2+F*B^-3 ... 2011-04-15T05:40:49 in standard number systems, B is an integers and S is the set of non-negative integers less than B 2011-04-15T05:41:05 but there is nothing wrong with making either of those anything we like :) 2011-04-15T05:41:46 So you take the set of real number in pi base, and a subset of them is in bijection with n. And the element of this subset have finite string writing in that base. 2011-04-15T05:42:29 yes 2011-04-15T05:42:55 if I understand you correctly 2011-04-15T05:42:58